In the days before your contest, make sure that your tuning is spot on, and take note of how much playing it takes for your drones and chanter reed to settle in and become steady and how long they stay that way. Make sure you give yourself enough time before your contest for that to happen, and leave some extra time in case of emergency.

Practice, practice, practice: focus on those points that are still rough.

__________________"Gentlemen, we are going to chase perfection, knowing full well we will not catch it, because nothing is perfect. But we are going to relentlessly chase it, because in the process we will catch excellence. I am not remotely interested in just being good."
- Vince Lombardi

In the days before your contest, make sure that your tuning is spot on, and take note of how much playing it takes for your drones and chanter reed to settle in and become steady and how long they stay that way. Make sure you give yourself enough time before your contest for that to happen, and leave some extra time in case of emergency.

Are there any rules of thumb regarding how long it should take? Mine seem to settle down in just a few minutes, and they don't seem to change much from day to day if I stay in my house.

I do notice that my chanter tuning changes a lot depending on the weather.